X-rays and other high energy radiation, such as extreme ultraviolet (EUV) radiation behave differently from other forms of electromagnetic radiation such as visible light. For example, containment of X-ray radiation and/or focusing of this and other types of high energy radiation is much more difficult than with visible light. Special considerations must be taken into account in applications utilizing X-ray and other types of high energy radiation. For example, X-ray imaging systems are particularly difficult to design because of the way in which X-rays interact with matter.
Generally speaking, X-rays that impinge at a normal angle of incidence on any material are largely absorbed rather than reflected. Therefore, normal incidence mirrors used for optical imaging systems, associated with visible wavelengths, are not useful for X-ray imaging systems. Any refracting imaging system, such as standard optical imaging systems using lenses, which has elements sufficiently thin to transmit X-rays, have extremely long focal lengths, which are not practical for laboratory applications.
Many materials have an index of refraction (n) that is less than 1 at X-ray wavelengths. For example, the index of refraction at X-ray wavelengths for many materials may be expressed as a complex number as defined by Equation 1 below:
 n=1−d−ib  (1)
where d represents absorption of the material and b represents the phase shift of the material, both dependent on the wavelength of the incident X-rays. Thus, as can be seen with reference to Equation 1 above, if d is greater than 0 and b is approximately 0, then the index of refraction (n) is less than 1. Because of this property, it is possible for an X-ray, which is traveling in a medium having an index of refraction of unity (i.e., n=1) such as a vacuum, to undergo “total external reflection,” for certain angles of incidence. Total external reflection is analogous to “total internal reflection” commonly associated with visible wavelengths of light and governed by Snell's law.
For X-rays to undergo total external reflection, when traveling from a vacuum having an index of refraction of 1, to a material for which the index of refraction is less than 1, certain conditions must be met. These conditions are defined by Snell's law, which states that X-rays will undergo total external reflections for angles θ, where:θ<θc  (2)and where:cos(θc)=1−d  (3)where d is the material parameter associated with the index of refraction at X-ray wavelengths of the material upon which the X-ray is incident, and θc is the critical angle for total external reflection. The critical angle may also be approximated by Equation 4 below:θc≈√{square root over (2d)}  (4)
The parameter d of the index of refraction (n) is proportional to the atomic number (Z). Thus, the critical angle θc is also essentially proportional to the atomic number of the material upon which the X-rays are incident. Therefore, materials having high atomic numbers reflect X-rays more efficiently than materials having low atomic numbers (i.e., the critical angle θc is larger for materials with a higher atomic number Z). For example, gold and nickel are commonly used as reflecting materials for X-rays. The critical angle θc for X-rays incident upon these elements, where the X-rays have an energy of approximately 1 keV, is about 1°. Therefore, according to Equations 2 and 3 above (and based on Snell's law), X-rays having an energy level of 1 keV would experience total external reflection as long as they were incident at an angle less than about 1°. Therefore, from the above, it can be seen that any system used to reflect X-rays would necessarily make use of small angles of incidence between the X-rays and the reflecting material.
Many advances in X-ray optics have come in the field of astronomy. Astronomers have used various techniques to image X-ray radiation from astronomical sources using large telescopes. For example, one method of focusing X-rays in astronomical telescopes has been proposed, which utilizes a set of non-parallel flat metal foils set at correct angles to focus incident X-ray radiation for proper imaging. One particular type of such X-ray imaging is known as “lobster-eye” optics, named after the construction of a lobster's eye, as found in nature. An in-depth discussion of lobster-eye optics can be found in Instrumentation for a Next-Generation X-Ray All-Sky Monitor; A. G. Peele, Code 662, available from the Laboratory for High Energy Astrophysics at the Goddard Space Flight Center in Greenbelt, Md.
X-ray optics used in astronomical devices, such as telescopes, are typically large assemblies, usually on the order of about 300 mm3. Such large optic devices serve to collect the maximum possible radiation from weak, distant sources. While such large devices are ideal for use in space with astronomical applications, as they can be easily maneuvered there, they are cumbersome and difficult to use in any type of earth-bound laboratory applications. However, the abilities of such devices could be useful in laboratory applications.
Therefore, it would be desirable to create a miniaturized version of such collector optics for X-rays and other high energy radiation for use in laboratory applications. These laboratory-sized, miniature collector optics should exhibit similar performance advantages to their larger astronomical cousins, but without the cumbersome size generally associated with larger optics.